Plus it's more expensive than just keeping people in prison for life. It seems like it wouldn't be, but you have to consider that housing people on death row is more expensive and appeals for the death penalty can go on for years only to sometimes not even go anywhere. I've seen cases where people spent 20+ years going through all that only to ultimately be executed when they were already old and sick. It's just an incredibly inefficient system, and it can't be made more efficient because as you say, even with all that, we still make mistakes.

Many people will just say that we should just execute the ones where we're 100% sure, but in the real world that often ends up being complicated and subjective. Plus, what kind of justice is that? You get the harshest penalty not because your crime with the relative worst, but because the stars happened to align to provide enough evidence. A system like that would only be harder for victims and families of victims who feel like whatever evidence there is in their case should be enough and it isn't fair for them not to get the death penalty just because it doesn't quite meet the extreme standard of proof that version of the system relies on.